The Gestalt of Heat Waves

guest post by Clyde Spencer

Abstract

T_max and T_min time-series are examined to look for historical, empirical evidence to support the claim that heat waves will become more frequent, of longer duration, and with higher temperatures than in the past. The two primary parameters examined are the coefficient of variation and the difference between T_max and T_min. There have been periods in the past when heat waves were more common. However, for nearly the last 30 years, there has been a reversal of the correlation of increasing CO₂ concentration with the T_max coefficient of variation. The reversal in differences in T_max and T_min indicate something notable happened around 1990.

Introduction

There was much in the press this Summer about the ‘global’ heat waves, particularly in France and Greenland. For an example of some of the pronouncements, see here. The predictions are that we should expect to see heat waves that are more frequent and more severe because of Anthropogenic Global Warming, now more commonly called “Climate Change.” The basis for the claim is unvalidated Global Climate Models, which are generally accepted to be running to warm. The simplistic rationale is that as the nights cool less, it takes less heating the next day to reach unusually high temperatures. Unfortunately, were that true, that would lead one to conclude that heat waves should never stop.

One agency that hasn’t erased the 1930s heat is the US Environmental Protection Agency. It clearly shows the 1930s with the largest heat wave index values!

Fig. 1. U.S. Annual Heat Wave Index, 1895-2015

https://www.epa.gov/climate-indicators/climate-change-indicators-high-and-low-temperatures

If the predictions of worse future heat waves were valid, one might expect to be able to discern a change occurring already, inasmuch as it is commonly accepted that Earth has been warming at least since the beginning of the Industrial Revolution. That is, if the Summer heat waves are occurring more frequently, and they are getting hotter, one might expect that the maximum daily temperatures would exhibit larger statistical variance.

Because humans live on land, and we are concerned about the impact on humans, such as comfort and excess heat-related deaths, it would seem to be most appropriate to look at just air temperatures over land. There is an unfortunate tendency in the climatology community to conflate sea surface temperatures with land air temperatures, which tends to dampen changes because it takes a lot more energy to change the temperature of water than air or even land. Thus, with more than 70% of the surface of the Earth covered with water, small changes or trends in energy will be more difficult to identify in the weighted-averages of water and land temperatures.

Analysis

To explore the situation, I used the Berkeley Earth Surface Temperature (BEST) project data. I wanted to get as close as reasonable to the raw data, minimizing the averaging that us usually employed in such data, and which raises concerns about subsequent statistical analysis. To that end, I downloaded an experimental data set that has the maximum and minimum daily air temperatures for the land-only surface of Earth. Figure 2, below, shows the coefficient of variation (CoV) of the maximum daily temperatures (T_max) as a time-series from 1880 through mid-2019. There are two traces shown: 1) a 30-year moving-average* of the standard deviation (SD) divided by the 30-year arithmetic mean, with daily steps; 2) a 1-year moving-average of the SD divided by the annual arithmetic mean, with daily steps. The division by the mean normalizes the SD, creating the CoV.

I converted the BEST temperature anomalies to estimated Celsius temperatures by adding the calculated 1951 through 1980 average T_max, to avoid an issue of dividing by zero_. I then converted the temperatures to the Kelvin scale to allow the T_max and T_min CoVs to be comparable. The metadata accompanying the T_max temperatures shows the estimated uncertainty of the baseline mean (14.41° C) to be ±0.11° C. Strictly speaking, the precision of the calculated anomalies should then be no greater than that value, and probably less, taking into account the uncertainty of individual measurements from which the anomalies are obtained. Nevertheless, BEST reports the anomalies to 3-significant figures to the right of the decimal point, rather than just the one (1) warranted. Ignoring that issue, and moving on ―

The annual moving-average of the T_max CoV is not particularly informative, other than showing large annual changes in what is essentially the standard deviation. However, the 30-year moving-averages smooths the data considerably, albeit truncating the first and last 15 years of the data. Between about 1895 and 1950, there is no obvious trend. However, after that, the CoV shows a distinct upward trend as might be expected if Summer heat waves were increasing in frequency, duration, and/or temperature. However, something unexpected shows up around 1996 – the CoV starts to decline! The annual CoV values also suggest that there is a decline after about 2000. Surprisingly, the infamous 1930s U.S. heat wave is only weakly reflected in the annual T_max CoV.

Fig. 2. T_max Coefficient of Variation Time-Series (http://berkeleyearth.lbl.gov/auto/Global/Complete_TMAX_daily.txt)

Fig. 3. T_min Coefficient of Variation Time-Series (http://berkeleyearth.lbl.gov/auto/Global/Complete_TMIN_daily.txt)

Interestingly, the CoV moving-average time-series for the T_min looks different, as shown in figure 3, above. As with the T_max time-series, it is a 30-year moving-average, with daily increments. Essentially, there is a decline in the variance from at least the mid-1890s, to about 1952, followed by an increase until about 1990, and then a return to the decline, at about the initial rate. The declines can be explained in the context of Earth’s radiative cooling being impeded by increasing ‘greenhouse gases.’ That is, it doesn’t get as cold at night, thereby decreasing the diurnal temperature drops, and consequently the T_min variance. The almost 40-year interruption in the decline is a little more difficult to explain because there has been no similar change in the accumulation of CO₂ in the atmosphere! (See Fig. 6, below.) That is a suggestion that any effects of long-lived CO₂ are over-ridden easily, possibly by aerosols, short-lived clouds, and water vapor, if not actually being the dominant drivers.

What is happening? To explore further, I examined the most recent T_max and T_min data from BEST. Because the daily data are so noisy, I decided to use the monthly time-series to examine the behavior of the temperatures.

Fig. 4. Monthly Averages of High and Low Temperatures Time-Series

(http://berkeleyearth.lbl.gov/auto/Global/Complete_TMAX_complete.txt)

[ I have addressed the issue of temperature changes previously, here: https://wattsupwiththat.com/2015/08/11/an-analysis-of-best-data-for-the-question-is-earth-warming-or-cooling/ ]

Again, Figure 4 is not very informative. It looks as though there may have been a slight increase in the slope of T_max after about 1975, which is difficult to attribute to the effects of CO₂. The rise in T_min may have decreased slightly after about 1998, with the exception of the 2016 El Niño. Plotting the anomalies [not shown], instead of actual temperatures, accentuates the post-1975 increase in the slope of T_max; however, the T_min appears more uniform. Note that the theory of ‘Greenhouse Gas’ warming predicts that the effects should be most apparent in the T_min. However, neither provides insight on what is happening with the CoVs around 1990!

However, a time-series plot of the monthly data showing the differences between T_max and T_min is much more interesting! As reported earlier, the difference has been declining since about the beginning of the 20^th Century. However, as with the CoVs, there is a distinct change about 1990! After a decline in the differences for about a century, the differences start to increase. The 3^rd-order polynomial regression, shown in purple, is of no particular importance other than to accentuate the change in the difference between the high and low temperatures. Albeit, it is suggestive of a possible 200-year cycle.

It appears that something subtle happened about 30 years ago that isn’t readily apparent in temperature (or temperature-anomaly) data alone. Figure 4 indicates that T_max and T_min are both increasing. Inasmuch as T_max is much larger than T_min, it will tend to dominate the resulting change, for a similar percentage change in both. It appears that both T_max and T_min were impacted similarly by the 2016 El Niño. The slope of T_max is larger than T_min between about 1985 and 2005. If T_max is increasing more than T_min, then it would argue against CO₂ being the primary driver of global warming!

Fig. 5. High and Low-temperature Difference Time Series

The question is, “What is causing the changes around 1990, and is it of any climatological significance?” One possible explanation is that the apparent change in temperature relationships is somehow an artifact of processing; however, I’m not familiar enough with the details of the BEST processing methodology to speculate just how this might occur. Ignoring the rules of precision and error propagation comes to mind though.

Fig. 6. CO₂ Concentration from 1958 through 2019

(http://scrippsco2.ucsd.edu/data/atmospheric_co2/primary_mlo_co2_record)

Figure 6 is a plot of the Mauna Loa measurements of CO₂, from Scripps Oceanographic Institute. Looking at the figure, there seems to be little to explain the behaviors noted above other than a slight apparent decrease in the growth rate of CO₂ after about 1990, for about two or three years. That is, if CO₂ is the main driver of temperature changes, there doesn’t seem to be anything in the behavior of the CO₂ concentrations that would obviously explain the recent long-term decline in the CoVs or the differences in T_max and T_min.

Assuming that the demonstrated CoV behavior is not an artifact and is real, the examined data suggest that if the global-average high temperatures are increasing, a consequence might be increased frequency or severity of heat waves. However, figures 2 and 4 only show the effects of the El Niño phenomenon, at best.

Summary

Extrapolations are always fraught with risk. However, based on the behavior of the T_max CoV, which appears to be declining, there does not seem to be strong empirical support for the prediction that future heat waves will be worse and more frequent than in the recent past.

Clearly, T_max has increased in the last 40-odd years. However, the CoV peaked about 30 years ago, and appears to still be in decline, based on the annual CoV values. Because T_max is typically the result of direct solar heating, a decline in the so-called ‘solar constant’ variance could result in a decline in the T_max CoV.

While T_min is clearly increasing, almost monotonically, the CoV suggests that the increase is by increasing the floor, or base level, of the minimum temperatures.

One might be tempted to dismiss the effects that I have illustrated as being so small as to be inconsequential. However, the temperature differences, and the 30-year moving-average standard deviations, on which the CoVs are based, have a long-term duration and a magnitude comparable to several decades of average global temperature change. I believe that an explanation is warranted. Do any of the Global Climate Models show these secondary effects?

I would like to invite thoughts on the behavior of the coefficient of variation, and differences in the high and low temperatures, with respect to global temperature changes.

References

C. D. Keeling, S. C. Piper, R. B. Bacastow, M. Wahlen, T. P. Whorf, M. Heimann, and H. A. Meijer, Exchanges of atmospheric CO2 and 13CO2 with the terrestrial biosphere and oceans from 1978 to 2000. I. Global aspects, SIO Reference Series, No. 01-06, Scripps Institution of Oceanography, San Diego, 88 pages, 2001.

*It is more accurate to refer to the CoVs as a “sliding sample” because only the denominator is actually a moving average.